Optimization

Abstract

In a wide range of source separation problems, large-scale optimization of various kinds of objective functions needs to be performed. The aim of this chapter is to introduce the theoretical background which makes it possible to develop efficient algorithms allowing to successfully address these problems. This chapter will be mainly focused on nonlinear optimization tools for dealing with convex and nonconvex problems. Proximal tools, parallel splitting techniques, Majorization-Minimization strategies and alternating minimization approaches will be presented. Related numerical algorithms adapted to the large-scale context will also be given. The chapter also considers the case of constrained optimization problems where constraints such as non-negativity and sparsity are imposed. Illustrations of these methods on some problems of physical-chemical sensing will be provided.